Calibration curves
HPLC, GC, ICP, UV–Vis, ELISA or any calibration. Fit the standards, read off your samples with dilution factors and confidence intervals, and check back-calculated recovery, LOD and LOQ.
How the calibration works
Chromatographic and spectroscopic calibrations are usually linear, often with 1/X or 1/Y weighting because the scatter grows with concentration. Immunoassays are sigmoidal, so the four-parameter logistic is used:
Y = D + (A − D) / (1 + (X/C)B)
A is the signal at zero concentration, D the signal at saturation, C the inflection point and B the slope. The 5PL adds an asymmetry exponent G. Because the scatter grows with the signal, 1/Y² weighting keeps the low standards accurate.
Interpolation inverts the fitted curve analytically. The 95% interval of each sample combines the curve's parameter covariance (delta method) with the standard error of the sample's replicates.
Quality checks: back-calculated recovery of each standard (accepted within 80–120%), replicate CV, samples outside the calibrated range, and LOD/LOQ from the blank mean + 3 SD and + 10 SD.
Validated against SciPy for weighted and unweighted fits. Validation report.